1. 3/2003 Rev 1 II.2.8 – slide 1 of 42 IAEA Post Graduate Educational Course Radiation Protection and Safe Use of Radiation Sources Part IIQuantities and Measurements Module 2Dosimetric Calculations and Measurements Session 8Doses from Neutron Sources Session II.2.8

2. 3/2003 Rev 1 II.2.8 – slide 2 of 42 Overview  Principles of neutron dose calculation will be discussed  Students will learn about fast and thermal neutron interactions with tissue; dose calculation from neutron beams, neutron point sources, fast neutrons, thermal neutrons  Example problems illustrating neutron dose calculation will be worked

3. 3/2003 Rev 1 II.2.8 – slide 3 of 42 Content  Fast and thermal neutron interactions with tissue  Dose from fast neutrons  Dose from thermal neutrons  Dose from neutron charged particle and gamma ray emissions  Example problems calculating dose from neutron beams  Example problems calculating dose from neutron point sources, including calibration sources, criticalities, and accelerators

4. 3/2003 Rev 1 II.2.8 – slide 4 of 42 Tissue Dose From Neutrons  Dose from fast neutrons is primarily due to elastic scattering with hydrogen  Dose from thermal neutrons is due to two reactions, primarily:  14 N(n,p) 14 C  1 H(n,  ) 2 H

5. 3/2003 Rev 1 II.2.8 – slide 5 of 42 Dose from Fast Neutrons  In case of elastic scattering, scattered nuclei dissipate their energy in the immediate vicinity of the primary neutron interaction  This is called the “first collision dose” and is entirely determined by the primary neutron flux  The scattered neutron is not considered after the primary interaction

6. 3/2003 Rev 1 II.2.8 – slide 6 of 42 Dose from Fast Neutrons For fast neutrons, the first collision dose is given by: D n (E) = where:  = neutron flux, n/cm 2 /sec E = neutron energy, ergs ENiifiENiifiENiifiENiifi 10 4 ergs g Gy

7. 3/2003 Rev 1 II.2.8 – slide 7 of 42 Dose from Fast Neutrons N i = atoms per gram of the i th element  i = scattering cross section of the i th element for neutrons of energy E in barns (x10 -24 cm 2 ) element for neutrons of energy E in barns (x10 -24 cm 2 ) f i = mean fractional energy transfer to scattered atoms of mass M atomic mass units during collision with a neutron of m atomic mass units

8. 3/2003 Rev 1 II.2.8 – slide 8 of 42 Mean Fractional Energy Transfer For isotropic scattering of fast neutrons, the average fraction of energy lost in an elastic collision with a nucleus of atomic mass number M is given by: f = (M + 1) 2 2M

9. 3/2003 Rev 1 II.2.8 – slide 9 of 42 f Values for Tissue Element N (atoms/g) f H 6.70 x 10 22 0.500 C 4.18 x 10 21 0.142 N 1.17 x 10 21 0.124 O 2.93 x 10 22 0.111

10. 3/2003 Rev 1 II.2.8 – slide 10 of 42 Sample Problem 1  What is the absorbed dose rate to soft tissue from a beam of 5 MeV neutrons whose intensity is 2000 n/cm 2 sec?  Given: scattering cross sections of each of the tissue elements for 5 MeV neutrons are shown in table in next slide

11. 3/2003 Rev 1 II.2.8 – slide 11 of 42 Sample Problem No. 1 Element  (cm 2 ) H 1.5 x 10 -24 C 1.65 x 10 -24 N 1.00 x 10 -24 O 1.55 x 10 -24 Scattering Cross Sections in Tissue for 5 MeV Neutrons

12. 3/2003 Rev 1 II.2.8 – slide 12 of 42 Solution to Sample Problem No. 1 Substituting the values for hydrogen into the equation, we have: 8.05 x 10 -8 Gy sec hr 2.9 x 10 -4 Gy = = 1.6x10 -6 erg MeV 5 MeV n 6.7x10 22 atoms g 1.5x10 -24 cm 2 atom cm 2 -sec 2000 n 10 4 ergs g Gy x x 0.5 x x x DH =DH =DH =DH =

13. 3/2003 Rev 1 II.2.8 – slide 13 of 42 Solution to Sample Problem No. 1  In a similar manner, the dose would be calculated for 5 MeV neutron interactions with C, N, and O  The total dose is found to be 3.2 x 10 -4 Gy/hr  Thus, 5 MeV neutron interactions with H contributed about 89% of the the total tissue dose!  It should be noted that this calculation was performed for a monoenergetic neutron beam

14. 3/2003 Rev 1 II.2.8 – slide 14 of 42 Dose from Thermal Neutrons The dose rate from the 14 N(n,p) 14 C reaction can be calculated as follows: D (n,p) =  N  Q x 1.6 x 10 -6 erg/MeV where:  = thermal flux, n/cm 2 /sec N = nitrogen atoms per gram tissue (1.17x10 21 )  = nitrogen absorption cross section (1.75x10 -24 cm 2 ) Q = energy released by the reaction (0.63 MeV) 10 4 erg/g/Gy

15. 3/2003 Rev 1 II.2.8 – slide 15 of 42 Sample Problem No. 2 Calculate the dose rate from the 14 N(n,p) 14 C reaction from an average total body exposure rate of 10,000 thermal neutrons per cm 2 per second.

16. 3/2003 Rev 1 II.2.8 – slide 16 of 42 Solution to Sample Problem No. 2 = 2.1 x 10 -9 Gy/sec = 7.56 x 10 -6 Gy/hr 1.6x10 -6 erg MeV 0.63 MeV n 1.17x10 21 atoms g 1.75x10 -24 cm 2 atom cm 2 -sec 10 4 n 10 4 ergs g Gy x x x x D n,p =

17. 3/2003 Rev 1 II.2.8 – slide 17 of 42 Dose from Thermal Neutrons  The dose rate from the 1 H(n,  ) 2 H reaction can be calculated based on the following:  This reaction is equivalent to having a gamma-emitting isotope uniformly distributed throughout the body  It results in what is called an “autointegral gamma-ray dose”

18. 3/2003 Rev 1 II.2.8 – slide 18 of 42 Dose from Thermal Neutrons The specific activity of this distributed gamma source, the number of reactions per second per gram of tissue, is given by: A =  N where:  = thermal neutron flux, n/cm 2 /sec N = No. of hydrogen atoms per gram of tissue (6.7x10 22 )  = hydrogen absorption cross section (0.33x10 -24 cm 2 )

19. 3/2003 Rev 1 II.2.8 – slide 19 of 42 Autointegral Gamma-Ray Dose Rate For a gamma-ray emitter uniformly distributed in the body, the autointegral gamma-ray dose rate may be calculated by the following equation: D  = C  g Gy/hr where: C = the concentration of the gamma emitter (Bq/cm 3 )  = source strength (Gy/hr per Bq at 1 cm) g = average geometry factor (cm)

20. 3/2003 Rev 1 II.2.8 – slide 20 of 42 Sample Problem No. 3 Calculate the absorbed dose rate to the standard man from the 1 H(n,  ) 2 H reaction due to an average total body exposure rate of 10,000 thermal neutrons/cm 2 /sec. Given: g (70 kg, 170 cm) = 126  (2.23 MeV photons ) = 2.70 x 10 -9 Gy-cm 2 /Bq-hr

21. 3/2003 Rev 1 II.2.8 – slide 21 of 42 Solution to Sample Problem No. 3 Calculate the “specific activity” from the 1 H(n,  ) 2 H reaction in tissue: 10 4 n cm 2 - sec 6.7 x 10 22 atoms g 3.3 x 10 -25 cm 2 atom 1 g cm 3 C = xxx = 221 photons = 221 Bq/cm 3 sec – cm 3

22. 3/2003 Rev 1 II.2.8 – slide 22 of 42 Solution to Sample Problem No. 3 Thus, the absorbed dose rate from gamma emission in tissue due to the 1 H(n,  ) 2 H reaction is given by: D  = C  g Gy/hr D  = C  g Gy/hr = 7.5 x 10 -5 Gy/hr 221 Bq cm 3 2.70 x 10 -9 Gy- cm 2 Bq-hr D  = 126 cm xx

23. 3/2003 Rev 1 II.2.8 – slide 23 of 42 Sample Problem No. 4 16 N calibration sources are commonly used at nuclear power stations. The source generates 16 N via the ( ,p) reaction, using 5.92 x 10 9 Bq of 244 Cm and 13 C. Calculate the total neutron dose equivalent rate at 1 m from the source.

24. 3/2003 Rev 1 II.2.8 – slide 24 of 42 Sample Problem No. 4 Given: Neutron source strength = 2.0 x 10 5 n/sec Neutron energy = 2.5 MeV Neutron flux to dose equivalent conversion factor (k) = 20 n/cm 2 /sec = 2.5 x 10 -5 Sv/hr Source is a point source

25. 3/2003 Rev 1 II.2.8 – slide 25 of 42 Solution to Sample Problem No. 4 The total neutron dose rate at 1 m is given by: D n = k where: S n = source strength r = distance from source to receptor k = neutron flux to dose equivalent rate conversion factor SnSnSnSn 4r24r24r24r2

26. 3/2003 Rev 1 II.2.8 – slide 26 of 42 Solution to Sample Problem No. 4 Solving the equation, we have: 4  (100 cm) 2 2.0 x 10 5 n/sec D n = x 2.5 x 10 -5 Sv/hr 20 n/cm 2 /sec = 2.0 x 10 -6 Sv/hr

27. 3/2003 Rev 1 II.2.8 – slide 27 of 42 Sample Problem No. 5 You are the health physics manager at a uranium fuel reprocessing facility. Building A includes a tank farm used to process highly enriched uranium. During a batch-processing operation in Building A, a technician violates standard operating procedures, which leads to a critical geometry in a small tank. A criticality occurs which releases 1.0 x 10 16 fissions.

28. 3/2003 Rev 1 II.2.8 – slide 28 of 42 Sample Problem No. 5 The plant manager is standing behind a 30.5 cm polyethylene shield and he is 3 meters from the center of the tank. Calculate the neutron dose equivalent in Sv to the plant manager during the Building A criticality.

29. 3/2003 Rev 1 II.2.8 – slide 29 of 42 Sample Problem No. 5 Given: Density of the polyethylene shield is 1.4 g/cm 3 Each fission event produces 3 neutrons The neutron spectrum for the criticality is represented by a dose conversion factor of 2.5 x 10 -5 Sv/hr per 20 neutrons/cm 2 -sec

30. 3/2003 Rev 1 II.2.8 – slide 30 of 42 Sample Problem No. 5 The mean neutron energy of the spectrum is 2.5 MeV The neutron dose attenuation factor for 2.5 MeV neutrons through 30.5 cm of polyethylene is 0.005 and the buildup factor is one The criticality is adequately represented by a point source and it lasts one hour

31. 3/2003 Rev 1 II.2.8 – slide 31 of 42 Solution to Sample Problem No. 5 The general equation for the neutron dose equivalent in this example is: N fissions  k e -  t B 4r24r24r24r2 Dn =Dn =Dn =Dn = where: N fissions = 1.0 x 10 16 k = 2.5 x 10 -5 Sv/hr per 20 neutrons/cm 2 -sec B = 1 e -  t B = 0.005 R = 3 m = 300 cm  = number of neutrons per fission = 3

32. 3/2003 Rev 1 II.2.8 – slide 32 of 42 Solution to Sample Problem No. 5 = 4.5 x 10 -2 Sv 1 hr 3600 sec 0.005 x (1.0x10 16 fissions)x(3 ) (4)x(3.14)x(300 2 cm 2 ) Dn =Dn =Dn =Dn = 2.5 x 10 -5 Sv hr 20 neutrons cm 2 -sec neutronsfission x x

33. 3/2003 Rev 1 II.2.8 – slide 33 of 42 Sample Problem No. 6 A linear accelerator (LINAC) bombards a tritium target with a 25  A beam of 2.5 MeV protons. This produces 1.2 MeV neutrons via the 3 H(p,n) 3 He reaction. Calculate the neutron dose equivalent rate in Sv/hr at a point 40 cm away from the target along the beam centerline.

34. 3/2003 Rev 1 II.2.8 – slide 34 of 42 Sample Problem No. 6 Given: Production rate = 1.8 x 10 -6 neutrons/proton 6.24 x 10 18 protons/amp-sec Dose conversion factor = 3.5 x 10 -10 Sv cm 2 n -1

35. 3/2003 Rev 1 II.2.8 – slide 35 of 42 Solution to Sample Problem No. 6 Assuming that the distribution of neutrons is isotropic, the dose equivalent rate can be written as: D n = IKk 1 P(DCF) (4  r 2 )

36. 3/2003 Rev 1 II.2.8 – slide 36 of 42 Solution to Sample Problem No. 6 where: I = proton beam current = 25.0 x 10 -6 A k = charge/proton = 1.602 x 10 -19 coulomb/proton K = 1/k = 6.24 x 10 18 protons/A-sec k 1 = time conversion factor = 3600 sec/hr P = neutron production rate = 1.8 x 10 -6 neutrons/proton DCF = dose conversion factor = 3.5 x 10 -10 Sv cm 2 n -1 r = distance from the target = 40 cm

37. 3/2003 Rev 1 II.2.8 – slide 37 of 42 Solution to Sample Problem No. 6 Therefore, = 1.8 x 10 -2 Sv/hr (25.0x10 -6 A) x (4  40 2 cm 2 ) 3600 sec hr 1.8 x 10 -6 n proton 3.5x10 -10 Sv cm 2 n 6.24x10 18 protons A-sec x x D n = 4.9x10 -6 Sv x 4.9x10 -6 Sv x sec =

38. 3/2003 Rev 1 II.2.8 – slide 38 of 42 Summary  Principles of neutron dose calculation were discussed  Students learned about fast and thermal neutron interactions; dose calculation from neutron beams, neutron point sources, fast neutrons, thermal neutrons; and worked example problems

39. 3/2003 Rev 1 II.2.8 – slide 39 of 42  Knoll, G.T., Radiation Detection and Measurement, 3 rd Edition, Wiley, New York (2000)  Attix, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986)  International Atomic Energy Agency, Determination of Absorbed Dose in Photon and Electron Beams, 2 nd Edition, Technical Reports Series No. 277, IAEA, Vienna (1997) Where to Get More Information

40. 3/2003 Rev 1 II.2.8 – slide 40 of 42  International Commission on Radiation Units and Measurements, Quantities and Units in Radiation Protection Dosimetry, Report No. 51, ICRU, Bethesda (1993)  International Commission on Radiation Units and Measurements, Fundamental Quantities and Units for Ionizing Radiation, Report No. 60, ICRU, Bethesda (1998) Where to Get More Information

41. 3/2003 Rev 1 II.2.8 – slide 41 of 42  Hine, G. J. and Brownell, G. L., (Ed. ), Radiation Dosimetry, Academic Press (New York, 1956)  Bevelacqua, Joseph J., Contemporary Health Physics, John Wiley & Sons, Inc. (New York, 1995)  International Commission on Radiological Protection, Data for Protection Against Ionizing Radiation from External Sources: Supplement to ICRP Publication 15. A Report of ICRP Committee 3, ICRP Publication 21, Pergamon Press (Oxford, 1973) Where to Get More Information

42. 3/2003 Rev 1 II.2.8 – slide 42 of 42 Where to Get More Information  Cember, H., Introduction to Health Physics, 3 rd Edition, McGraw-Hill, New York (2000)  Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8 th Edition, 1999 update), Wiley, New York (1999)  International Atomic Energy Agency, The Safe Use of Radiation Sources, Training Course Series No. 6, IAEA, Vienna (1995)